Analysis of a new pursuit-evasion game based on game theory

In this paper, we focus on a new pursuit-evasion game in which the evaders also act as intruders. We divide the game into two tasks. The first one is concerning about Intrusion, while the second one is about Safety of the evaders. Thus we formulate a multi-objective game model based on Nash Equilibrium of mixed strategies in order to find the Pareto Optimal Security Strategy for both kinds of agents. Our game model is a special one of zero-sum game, and we transform it to single-objective game by attaching weight to each single task. Our conclusion is that if the task of Safety is not considered, the evader can even hardly perform the task of Intrusion. When a little more weight is attached to the Safety, the evader can successfully fulfill the task of Intrusion while keeping safe. However, if too much weight is attached to Safety, though the stronger evader can keep itself safe, it can hardly perform the Intrusion task. These conclusions would be extended as some tips for military applications.